Understanding the Fatigue Notch Sensitivity of High-Strength Steels through Fracture Toughness

: This study presents an innovative approach for selecting high-strength materials for fatigue dimensioning parts, considering both fracture toughness and fatigue performance. Warm and hot forming processes enable the construction of high-strength parts above 1000 MPa with complex geometries, making them suitable for lightweight chassis in automotive and freight applications. This research reveals that high-strength steels can experience up to a 40% reduction in fatigue performance due to manufacturing defects introduced during punching and trimming. Fracture toughness has been proposed as a good indicator of notch sensitivity, with a strong correlation of 0.83 between fracture toughness and fatigue notch sensitivity. Therefore, by combining fracture toughness measurements and fatigue resistance obtained through the rapid fatigue test, it becomes possible to quickly identify the most fatigue-resistant materials to deal with defects. Among the nine materials analysed, warm-formed steels show promising characteristics for lightweight chassis construction, with high fatigue resistance and fracture toughness exceeding the proposed fracture threshold of 250 kJ/m 2 .


Introduction
Many metallic structures experience cyclic loading during their lifetime, which can potentially compromise their integrity, even if they are loaded below the yield strength of the material.A prime example of such structures are automotive chassis parts, which are exposed to high cyclic stresses during vehicle operation [1][2][3][4][5].Despite the high quality required for these parts, the need for greater transport efficiency and lightweight construction is driving innovation in the truck market [6,7].Currently, chassis parts are typically manufactured using mild-and high-strength low alloy (HSLA) steel sheets, which exhibit good mechanical properties but are not sufficient to achieve significant weight reductions.However, the industry can adopt the lightweighting strategies developed for the body in white components of passenger vehicles by using high-strength steels [8].Sheet-forming processes such as press-hardening or warm-forming can be employed to form high-strength steels, resulting in even lighter parts with complex shapes which can withstand higher loads.
Fatigue is a phenomenon in which plastic deformation accumulates due to cyclic loading, resulting in crack initiation, propagation, and eventual fracture of a component.This localised plastic deformation occurs at the most stressed site, which can be promoted by a poor component design or surface defects introduced during part manufacturing.In chassis parts, these surface irregularities are often introduced in the sheet shearing process (trimming, punching, etc.).It has been shown that the sheared edge morphology depends on various factors, including the material, punch geometry, shearing clearance, and tool wear [9,10].Some strategies have been developed to overcome such problems.Angled punches reduce the shearing forces but also the quality of the edge [11].The angle between the punch and the sheet induces lateral forces in the punch that varies the cutting clearance [12].Using worn tools or a high clearance leads to excessive plastic deformation, fracture angle, and burr, while sharp tools and small clearances may produce undesired burnish zones and secondary cracks [13].Moreover, the defects on the shear edge may compromise the sheet's formability if the next forming steps involve bending or stretching operations, resulting in edge cracks.This phenomenon is well known in sheet forming of high-strength materials; furthermore, it is named edge cracking.Frómeta et al. [14] showed that fracture toughness is a valuable parameter to rank the edge cracking resistance of high-strength steels and to evaluate the resistance to crack propagation.It has been shown that high-toughness steels have higher resistance to edge cracking [15].Similarly, the shape of the sheared edge affects the fatigue resistance of the components [16].Several authors have shown that the defects in the sheared edge govern fatigue resistance as they act as stress raisers and crack initiation points [17][18][19][20].Multiple solutions have been proposed to improve the fatigue resistance of the sheared edge, such as the two-stage shearing process.The technique leaves a cutting offset cut in a consecutive shearing operation resulting in a less damaged edge and better surface quality.The process highly improves the formability and fatigue resistance of the sheared material [21].Another technique relies on introducing compressive residual stresses to the sheared edge through shot-peening and coining processes [22][23][24].Although the fatigue results are improved, fatigue strength is still reduced after shearing the material, which is more relevant in materials with higher yield strength.In fact, the edge-cutting method is especially relevant in high-strength steels where the defects could decrease the fatigue resistance by more than 30-40% [25-27].
Numerous theories and methods have been developed to analyse the fatigue notch effect by using the concept of stress gradient [28,29].Nonetheless, obtaining the necessary data, such as fatigue threshold and fatigue limit, to input into these models remains time-consuming.Although thermographic technologies appear to facilitate the rapid determination of the fatigue limit for regular specimen shapes or notched geometries [30,31], it is important to note that the thermal signal may be influenced by external sources, which could compromise the analysis [32].This limitation can be overcome by employing the rapid testing method based on strain measurements [33].In this work, coupling this method with fracture toughness as an experimental tool is proposed to rapidly assesses the impact of notches on fatigue of high-strength steels.The aim is to expedite the material selection process for fatigue applications.

Materials
The nine investigated materials cover the primary microstructures of cold and hotrolled high-strength steel sheets, from ferrite-pearlite steel to a fully martensitic microstructure.The HSLA S500MC steel exhibits a ferritic-pearlitic microstructure such as the high-drawing quality mild steel MS300 but with a very fine dispersion of alloy carbides.The ferritic-bainitic matrix with martensite and austenite islands of the hot rolled complex phase (CP) steel HR800CP shows similar mechanical properties to the ferritic-bainitic S700MC.A good balance between formability and strength is achieved by the dual-phase steels combining a soft ferrite matrix with martensite islands, leading to excellent strain hardening and elongation at failure.Cold forming of DP1000 allows the production of parts with greater resistance than the HSLA steels; however, the high elevated stamping loads and the associated high springback hamper their application to form complex shape parts.One alternative is the warm forming process, a similar strategy to the well-known hot forming process but at lower forming temperatures and without reaching the austenitizing temperature (Ac 3 ).Both solutions are based on heating the material to increase its formability.In the hot forming, the material is heated above Ac 3 , hot-formed and die-quenched.This is the case of the studied fully martensitic press-hardened steel 22MnB5 (Figure 1d).Warm forming consists in heating the blank around 600 ºC for 4 min, warm forming, and air-cooling.The technology has the benefit of being able to form lighter and more complex components made of high-strength hot-rolled steel grades.A further advantage of this process is that no sheet coatings are required.Cracks in the coating produced by thermal mismatch affect the fatigue behaviour as these cracks act as fatigue initiation points as observed in press-hardening B steels [34].In the as-received condition, the WL750 grade presents a bainitic microstructure (Figure 1a).After warm forming, the alloying elements form fine dispersed alloy carbides in the bainitic matrix.The WL980 and WL1150 grades show a fully martensitic microstructure in the as-received condition, which form tempered martensite after the heat treatment as shown in Figure 1b,c, decreasing the yield strength and ultimate strength.The rough chemical composition of the investigated materials is given in Table 1.Conventional axial tensile tests were performed for the different microstructures in a universal testing machine according to ISO 6892 standard.The tensile specimens were machined transverse to the rolling direction.The results are reported in Table 2, with the microstructure corresponding to each steel grade.

Fatigue Tests
The fatigue strength was evaluated in terms of fatigue strength (σ f ) at 2•10 6 cycles, which is defined as the fatigue limit for the high cycle fatigue (HCF) regime [35] and is commonly used in the automotive industry [36].It was determined through the conventional testing method following the ISO 1099 recommendations.At least 15 specimens were used for each material in the staircase tests according to Dixon-Mood method [37].Moreover, the fatigue resistance of the warm-forming materials was determined by testing 3 specimens using the stiffness method described in the reference [38].The stepwise method consisted in increasing the maximum stress (σ max ) after a loading block of 6000 cycles.The stress is increased by 25 MPa between each block up to the fracture of the specimen, as schematically described in Figure 2. The test starts with a σ max of 50 MPa, which is below the expected σ f .The damage introduced during the test was monitored through the total strain range measurements (∆ε i ) performed at the beginning of the test when the material was non-damaged and after each fatigue block.∆ε i was measured at a nominal elastic stress of σ YS /2 using a loading-unloading rate of 5 MPa/s.The strain measurements were carried out using a 3D Digital Image Correlation (DIC) GOM Aramis SRX, Class 0.5 according to ISO 9513.The system was equipped with an external blue LED light to illuminate the painted specimen and avoid the effect of the ambient light of the laboratory.The exposure time was less than 5 ms, and the frame rate was 25 Hz.The cameras mounted onto the testing machine were calibrated before the test session using a coded panel of 150 mm by 120 mm.The facet size used was 11 × 11 pixels, and the initial length (L 0 ) of the virtual extensometer placed on the fatigue specimen was 20 mm.Once the specimen was broken, the strain progress rate (d∆ε i /dN) was evaluated to identify the three regimes linked to the fatigue damage: (i) incipient damage, (ii) microcrack formation, and (iii) macrocrack propagation.The regimes (i) and (ii) were used to quantify the fatigue damage (D) according to: where ∆ε p0 and ∆ε pf are the initial and final inelastic strains, respectively, and ∆ε p is the inelastic strain after each fatigue block.As shown in Figure 2c, the σ f was determined by the interception of the fitting line to the x-axis in the plot of the inelastic strains (∆ε p ) against the maximum stress (σ max ).The selected points for the fitting line are the points that describe the microcrack propagation.In this method, only three specimens were required to determine the fatigue limit in a short time.Staircase and rapid tests were performed at room temperature using a stress-controlled servo-hydraulic testing machine MTS 322 Test Frame.The loading frequency was set at 30 Hz with a sinusoidal wave.Thinner specimens were tested at a stress ratio (R = σ min /σ max ) of 0.1 to prevent buckling issues, while thicker specimens were tested at R = −1 to decrease the testing loads.The results obtained from tests at R = 0.1 were converted to −1 using the Gerber relation to allow for comparison purposes.
Fatigue resistance was evaluated for two different edge conditions: polished and sheared.The specimens with polished edges were machined perpendicularly to the rolling direction using an electro-discharging machine (EDM).Only the edges were ground and polished up to a R a < 0.2 mm, while the surface of the material was left in the as-rolled condition.The specimens with sheared edges were also machined perpendicularly to the rolling direction.For thin materials below 3 mm, a rigid trimming tool was used to obtain the dog-bone specimen geometry shown in Figure 3a, while for thicker ones, a rigid punching tool with a 10 mm punch diameter was used to obtain the open-hole specimen geometry depicted in Figure 3b.This strategy was used owing to the elevated loads required to shear thick highstrength steels.The stress concentration factors (K t ) were calculated through numerical modelling, and their values are presented in Figure 3.Both geometries in conventional tensile and in the normal location of failure onset exhibit a stress triaxiality of 0.33 at maximum force, which is in agreement with the results reported by several authors [39,40].The shearing clearances specified in Table 3 are commonly used in chassis parts to avoid burrs and excessive deformation of the edge [21,41].

Fracture Toughness Tests
The essential work of fracture (EWF) methodology was employed to measure fracture toughness.This method has been extensively used to describe the ductile fracture of thin and thick high-strength steels [42,43].Such ductile fracture results from combining two parameters that belong to the inner fracture process zone (FPZ) and the outer plastic region during ductile fracture.The work developed in the FPZ is named the essential work of fracture (W e ), which describes the required energy to create new fracture surfaces at the front of the crack tip, and then, it is proportional to the fractured area.On the other hand, the work dissipated in the outer plastic region is called the non-essential plastic work (W p ) and strongly depends on the deformed volume surrounding the fracture plane.Thus, the total work of ductile fracture can be expressed as: where w e is the specific essential work of fracture per unit of area, l 0 is the ligament length, t 0 is the specimen thickness, w p is the specific non-essential plastic work per unit of volume, and b is a shape factor that depends on the shape of the plastic region.Equation ( 2) can be normalised by the cross-section area resulting in the following: By plotting a series of w f for different ligament lengths (l 0 ), a linear fitting can be used to obtain w e as the intercept in the y-axis and the βw p as the slope, as shown in Figure 4.The w f values are experimentally obtained by measuring the area under the load-displacement curves (W f ) for each l 0 and dividing it by the cross-section l 0 t 0 .As previously described, the nature of w e makes it suitable to describe the crack propagation resistance of ductile steels, and conceptually, it is equivalent to the J-integral [44].The testing procedure described in CWA 17793 [45] was followed to conduct the tests.Double Edge Notched Tensile (DENT) specimens, as shown in Figure 5a, were utilised to test thin materials (t = 1.5-2 mm).The specimens were machined transverse to the rolling direction using electrical discharge machining (EDM), and a pre-crack of at least 0.5 mm was propagated in the root of the machined notches using a resonance fatigue testing machine at R = 0.1.The pre-cracked specimens were then loaded monotonically until fracture in a universal testing machine at a crosshead speed of 1 mm/min.A video extensometer with an L 0 of 50 mm directly measured the displacement on the specimen.The ligament lengths of the specimens ranged from 6 to 16 mm, and at least 3 specimens were tested up to fracture for each ligament length.For materials thicker than 2 mm, single edge notch bending (SENB) specimens were machined transverse to the rolling direction, as shown in Figure 5b.It is recommended to use the SENB geometry for thick materials to avoid asymmetrical pre-cracks that may lead to increased scatter and reduce the required maximum load to break the specimens [46].The specimens were fatigue pre-cracked at R = 0.1, following the guidelines of ASTM E1820 to avoid plasticity at the crack tip.A universal testing machine was used to test the specimens with a 3-point bending rig.The tests were conducted at a constant crosshead displacement of 1 mm/min.The crosshead displacement and the load were recorded during the test.

Influence of Sheared Edge Defects on Fatigue Resistance
Figure 6 depicts edge surface examples obtained using 3D profilometry for the S500MC and S700MC.The edges display the characteristic zones from the shearing process: the smooth or burnish zone and fracture zone [47].Despite the nearly identical shearing clearance, the shape of the punched edges differs significantly.In the case of S500MC, approximately one-third of the edge thickness belongs to the fracture zone, while the remaining two-thirds belong to the smooth zone.Conversely, for S700MC, the smooth zone only accounts for one-third of the punched edge, with the majority of the edge belonging to the fracture zone.
The observed differences in the proportions of sheared zones are closely linked to the material properties, including strength, fracture resistance, and thickness.The characteristics of the edge can have a significant impact on the fatigue resistance of the material due to the presence of irregularities such as microcracks or small defects within the fracture zone, the transition zone between the smooth and fracture zones, or the burr.These irregularities act as stress raisers, inducing crack initiation [48].Figure 7 illustrates a representative fractography observed in high-strength materials with a σ YS above 500 MPa.The fractography provides compelling evidence that edge irregularities serve as fatigue crack initiation sites.Notably, the fatigue origins are primarily situated at the fracture zone of the cut edge, and the resulting cracks propagate through the material in a transgranular manner.Conversely, the MS300 shows ductile fracture behaviour, which can be directly attributed to the significant plasticity induced within the material, as stated in Section 3.2.In this particular case, no conclusive evidence suggests that defects play a role in triggering crack initiation.Meanwhile, the roughness or defects on the as-rolled sheet surface govern the fatigue resistance of the edge-polished specimens.The cracks in both cases initiate and propagate in mode I, perpendicular to the loading direction.Table 3 presents the fatigue resistance of various materials under polished conditions, with the martensitic materials WL1150 and WL980 exhibiting the highest fatigue resistance, while the ferritic-pearlitic MS300 displays the lowest.This trend is consistent with the widely accepted notion that σf increases with increasing tensile strength (σUTS), as illustrated in Figure 8a [49].However, it is also acknowledged that increasing σUTS decreases the tolerance against small defects under fatigue loading [48,50].This fatigue sensitivity can be quantified by calculating the fatigue strength reduction factor (kf), which takes into account the fatigue resistance of the sheared and polished edge at 2 × 10 6 cycles: Values of kf close to 1 indicate low or no fatigue sensitivity to pre-existents defects.In contrast, lower kf values correspond to greater fatigue sensitivity to defects and, consequently, lower fatigue limit of defect-containing specimens.Figure 8b illustrates the plot of kf against σUTS for the studied materials, highlighting that σUTS is not the most effective indicator of fatigue sensitivity.In this case, 2 materials, S700MC and HR800CP, with sim- Table 3 presents the fatigue resistance of various materials under polished conditions, with the martensitic materials WL1150 and WL980 exhibiting the highest fatigue resistance, while the ferritic-pearlitic MS300 displays the lowest.This trend is consistent with the widely accepted notion that σ f increases with increasing tensile strength (σ UTS ), as illustrated in Figure 8a [49].However, it is also acknowledged that increasing σ UTS decreases the tolerance against small defects under fatigue loading [48,50].This fatigue sensitivity can be quantified by calculating the fatigue strength reduction factor (k f ), which takes into account the fatigue resistance of the sheared and polished edge at 2 × 10 6 cycles: Values of k f close to 1 indicate low or no fatigue sensitivity to pre-existents defects.In contrast, lower k f values correspond to greater fatigue sensitivity to defects and, consequently, lower fatigue limit of defect-containing specimens.Figure 8b illustrates the plot of k f against σ UTS for the studied materials, highlighting that σ UTS is not the most effective indicator of fatigue sensitivity.In this case, 2 materials, S700MC and HR800CP, with similar σ UTS values, exhibit different k f values.This phenomenon can be attributed to the fact that the fatigue resistance of sheared edge specimens is primarily determined by the material's ability to resist the propagation of edge defects.Therefore, as described in the subsequent paragraphs, the resistance to crack propagation, i.e., fracture toughness, should also be considered.
Table 3. Fatigue and fracture toughness results for the nine investigated materials: fatigue limit (σ f ) at R = −1 (results from tests at R of 0.1 are converted using the Gerber relation) for each edge condition, clearance (Cl), fatigue strength reduction factor (k f ), and fracture toughness (w e ).

Damage-Tolerant Fatigue Design Approach
The behaviour of materials containing defects can be addressed by employing a defecttolerant fatigue design approach, which assumes that defects can be treated as effective cracks that propagate once a certain threshold is exceeded.This approach is commonly rationalised within the framework of linear elastic fracture mechanics (LEFM), where a preexistent defect (a) propagates under cyclic loading (∆σ) once the threshold stress intensity factor range (∆K th ) is attained: where Y is a dimensionless factor related to the geometry of the crack.However, the application of LEFM is limited to the cyclic fracture resistance of a material when the small-scale yielding condition is dominant.This condition stipulates that the plastic zone at the crack tip (r c ) must be smaller than the defect size.When a/r c is greater than 10 (or r c /a < 0.1), the plastic zone is considered to be small, and the small-scale yielding condition is valid [51].The size of the cyclic plastic zone was determined by the Dugdale approach using the data from Tables 2 and 3 [52].
Based on the calculated r c /a values, the use of LEFM is limited to 22MnB5 and S700MC (r c /a < 0.1), as the plastic zone of the remaining materials is too large to satisfy the smallscale yielding conditions (r c /a between 0.12 and 0.29), with MS300 being clearly outside this regime (r c /a of 0.46).In such cases, the shear edge defects of these materials can be treated as mechanically small cracks as their size is comparable to the plastic zone [53], precluding the application of LEFM to describe their propagation.Instead, the propagation of such defects can be described using the √ area parameter proposed by Murakami et al. [54].Based on such an empirical approach-and considering that strength may be estimated from the Vickers hardness (HV)-some equations were proposed to estimate the length of the equivalent critical crack ( √ area critical ) from HV, such as the one presented below [55]: The equation can be employed to assess if the defects at the sheared edge for the studied material are sufficiently large to propagate under fatigue.Specifically, the √ area critical value was calculated for each material, with the σ UTS converted to HV according to ISO 18265.The defects at the sheared edge were quantified through the parameter R v , defined as the deepest valley from the surface profile, obtained via profilometry measurements at both the fracture and smooth zones.This parameter was established as an effective means of characterising the critical defect that initiates fatigue in press-hardened steels [34].R v ranges from 30 (for the S500MC) to 60 µm (for the HR800CP).Figure 9 depicts the estimated values of √ area critical .For the low strength MS300 (with σ UTS of 300 MPa), the calculated √ area critical is 70 µm, which is greater than the measured shear edge defects (R v = 49 ± 15 mm).This suggests that edge cracks in MS300 will not propagate, and therefore, that the fatigue resistance of sheared and polished specimens should be similar.This is consistent with the results presented in Table 3, where the fatigue resistance of the polished and trimmed conditions is identical.On the other hand, for steels with σ UTS above 500 MPa, the calculated √ area critical is lower than 10 µm, which is lower than the sheared edge defects.This means that such defects will propagate under fatigue, resulting in a lower fatigue limit for specimens with sheared edges.This agrees with the findings shown in Table 3.However, Figure 9 indicates that there is no clear correlation between √ area critical and σ f for the sheared specimens, which is illustrated by instances where the value of √ area critical is similar but the fatigue resistance is different.Hence, it is not recommended to rely solely on √ area critical as a reliable predictor of the fatigue resistance of sheared specimens.The new generation of high-strength steels, as the ones analysed here, have optimised microstructures to reach high toughness together with high strength, so the effect of both properties on fatigue resistance should be considered.Tough materials, evidenced as steels with w e > 250 kJ/m 2 in Table 3, exhibit high resistance to monotonic crack propagation, which could enhance fatigue performance.This contribution may be particularly significant in the case of sheared specimens, where defects are already present and most of the fatigue life is related to the cyclic propagation of these defects.

Relationship between Fracture Toughness and Fatigue Notch Sensitivity
The fatigue propagation of mechanically small cracks can be described by using an elastic-plastic fracture mechanics approach, as proposed by Dowling and Begley [56] through the cyclic J-integral (∆J) [57,58].This method has been successfully applied to describe the cyclic driving force in fatigue crack propagation of surface cracks in welds, which may be similar to edge defects [59].As ∆J is an extension of the monotonic J-integral introduced by Rice [60], w e (equivalent to J Ic ) can be used to understand fatigue crack propagation.Figure 10 illustrates how w e can effectively rank the fatigue sensitivity, k f .Both parameters show a strong positive correlation according to the calculated Pearson correlation coefficient (r) value of 0.83.Materials with low toughness (low values of w e ) are more sensitive to defects (low values of k f ), because of the scarce energy available to resist crack propagation of pre-existing defects.This indicates that low-toughness materials have high fatigue notch sensitivity and low damage tolerance.Conversely, tough materials with high values of w e exhibit low sensitivity to surface defects (k f close to 1), as the material offers high resistance to crack propagation.Therefore, the fatigue limit of polished and sheared specimens will be similar, indicating that high-toughness materials (w e > 250 kJ/m 2 ) have high damage tolerance and low fatigue notch sensitivity.This is mainly due to the higher fracture energy required to propagate the already nucleated defects.Frómeta et al., also reported this energy level of 250 kJ/m 2 as an indicator of high edge cracking resistance [14] and crashworthiness [43] in advanced high strength steels.

Implications on the Design of Fatigue-Relevant Parts
To select materials with high fatigue performance, it is important to consider both the fatigue limit and the fatigue notch sensitivity.Fracture toughness is a property that can represent the fatigue notch sensitivity, and thus, plotting the fatigue resistance of materials in the polished condition (σ f ) against their fracture toughness (w e ) provide valuable information for material selection (Figure 11).It is important to note that a moderate negative correlation (r = −0.31)has been observed, indicating a decrease in fatigue strength as fracture toughness increases.This tendency is similar with the observed inverse relationship between fracture toughness and yield strength [61].However, it is worth mentioning that the enhanced microstructures of new high-strength steels exhibit not only high yield strength but also higher fracture toughness values [14].These advancements challenge the traditional understanding of the relationship between fracture toughness and yield strength usually related to fatigue strength [62].Then, the ideal materials for fatigue dimensioning parts would be located in the upper right corner of the plot.The behaviour of the studied materials in this fatigue-toughness plot can be described as follows: • DP1000 and S700MC have high fatigue limits but low toughness (<250 kJ/m 2 ), resulting in low damage tolerance or high fatigue notch sensitivity;

•
The 22MnB5 steel shows excellent formability in hot conditions and superior fatigue resistance, making it a good candidate for lightweighting.However, its high sensitivity to defects (low fracture toughness) indicates that special attention must be paid during component designing and manufacturing.Similar behaviour is found for WL1150; • WL750, WL980, HR800CP, and S500MC exhibit high fatigue limits and low fatigue notch sensitivity, which postulate them as good candidates for chassis lightweighting strategies.
In general, warm-formed steels (WL780, WL980, WL1150) show a good combination of high fatigue limit and fracture toughness.This optimised performance, together with the high formability of these steel grades at the manufacturing temperatures, even for thick sheets, poses them as excellent candidates for truck chassis parts.

Conclusions
This study demonstrates that the fatigue resistance of the material, measured in polished specimens, and the fracture toughness, measured in the frame of elastic-plastic fracture mechanics, may be used in tandem to select high-strength material for lightweighting fatigue-dimensioning parts.The experimental results lead to the following conclusions: - The fatigue resistance of both edge-polished and sheared specimens can be measured in 3-4 h using the stiffness method; -The influence of the sheared edge quality on the fatigue resistance can be quantified by a fatigue strength reduction factor (k f ).Such factor accounts for the fatigue notch sensitivity; low values of k f around 0.  Funding: This research received no external funding.

Figure 2 .
Figure 2. Schematic representation for (a) fatigue specimen geometry; (b) successive fatigue blocks with increasing stress amplitude and strain measurements to determine the fatigue damage;(c) inelastic strain range (white rhombus) versus maximum stress to determine the fatigue limit through the fitting line.

Figure 3 .
Figure 3. Fatigue specimens with (a) trimmed edges (K t = 1.03) and (b) punched holes (K t = 2.42).Rigid tools designed to (c) trim and (d) punch specimens.The dimensions are expressed in mm.

Figure 4 .
Figure 4. Schematic representation for (a) DENT specimen geometry; (b) load (P)-displacement (δ) curves of each ligament length; (c) specific work of fracture (black square) versus ligament length to determine the specific essential work of fracture and non-essential plastic work through the fitting line.

Figure 5 .
Figure 5. Fracture toughness specimen geometries: (a) DENT and (b) SENB and (c) detail of the EDM notches with fatigue pre-cracks.The dimensions are expressed in mm.

Figure 6 .Figure 7 .
Figure 6.(a) Schematic of the shearing process and edge characteristics.Punched edge surface examples acquired through an optical profilometer for (b) S500MC and (c) S700MC.(d) Edge profiles obtained by 3D profilometry for the S500MC, S700MC, and HRCP800.

Figure 7 .
Figure 7. Representative fatigue crack initiation and propagation for polished specimens of (a) WL750 and (b) WL1150 and punched specimens of (c) WL 750 and (d) WL1150.Yellow arrows indicate the crack initiation sites in all the specimens.

Figure 8 .
Figure 8.(a) Fatigue resistance of polished specimens (σ f ) against tensile strength (σ UTS ) for the investigated steels.The dashed line is a visual guide to show the increasing trend of both properties.(b) Fatigue strength reduction factor (k f ) as a function of the tensile strength (σ UTS ).

Figure 9 .
Figure 9. Fatigue resistance of sheared specimens (σ f-sheared ) against estimated √ area critical for the investigated steels.

Figure 10 .
Figure 10.Fatigue strength reduction factor (k f ) as a function of fracture toughness (w e ).
5 mean high fatigue notch sensitivity or low fatigue damage tolerance, meanwhile values of k f close to 1 indicate low fatigue notch sensitivity or high fatigue damage tolerance; -The k f factor correlates well with the fracture toughness, determined by the essential work of fracture methodology, reporting a correlation coefficient (r) value of 0.83.Accordingly, tough materials such as the WL750 (w e = 344 ± 49 kJ/m 2 ) show low fatigue notch sensitivity, while low-toughness materials such as the 22MnB5 (w e = 159 ± 11 kJ/m 2 ) have high fatigue notch sensitivity.A w e of 250 kJ/m 2 can be defined as a threshold for a low fatigue sensitivity to surface defects, for the studied materials; -Despite the moderate correlation between fatigue and fracture toughness parameters (r = −0.31), the plot permits ranking of the material candidates to be used for a lightweight fatigue design of chassis parts.Following such results, the warm-formed steels stand out as one of the best candidates, showing good fatigue resistance above the reference material and fracture toughness higher than the w e threshold.

Figure 11 .
Figure 11.Fatigue resistance of polished specimens (σ f ) against fracture toughness (w e ) for the investigated steels.The dashed lines represent the reference fatigue resistance and the fracture toughness threshold.